CT based attenuation correction for SPECT

In order to obtain reliable quantitative images in SPECT, it is necessary to determine how attenuation by the overlying tissues and organs influence acquired data. Even without a need for quantification, the relationship FIG. 11. Geometry involved in CT. (a) Most CT scanners work with a fan beam geometry. (b) With extended axial extent. (c) For reconstruction parallel projections, data are rebinned prior to reconstruction. (d) Helical scans require interpolation to derive slice information from the acquired data.

between observed activities in tissues of different density and at different depths in the body is strongly influenced by attenuation and the inherent inconsistency of non-corrected projections. Historically in SPECT (as well as in PET), AC was based on transmission sources (either lines or points). In PET, the correction can be performed in the projection space before using FBP because the correction factor for a given projection element depends only on the properties of the attenuating object and not on the source localization. In SPECT, however, the correction also depends on the actual source depth. Therefore, the implementation in SPECT requires that the correction be included in an iterative reconstruction loop. Single photon emitters which have been used for attenuation measurements are ¹⁵³Gd and ¹³³Ba. However, due to the limited photon flux available from such sources, the acquisition time is considerable; and even when simultaneous acquisition could be used, the necessary corrections for the ‘cross-contamination’ between emission and transmission counts would significantly contribute to the noise.

In this regard, AC in SPECT using transmission sources has not been widely adopted in clinical use.

With the introduction of CT to SPECT systems, the adoption of AC has become more widespread. The information provided in a CT measurement is basically that of tissue specific attenuation and, compared to the results from transmission sources, this ‘μ map’ is essentially noiseless. The reconstructed CT image contrast owes its anatomical information to the fact that different tissues have slightly different composition and density, and therefore different (linear) attenuation coefficients. The standard Hounsfield unit (HU) of CT numbers is calculated from  a  linear  scaling  of  the  reconstructed  attenuation  coefficients,  assigning  the  values  −1000  to  air  and  0  to  water [37]. However, photon attenuation is strongly dependent on the photon energy, and therefore a ‘translation’

or ‘downscaling’ of the μ map is needed between the effective CT energy and the relevant photon energy used for emission imaging. For PET, one such translation for each CT energy suffices, since all nuclides used in PET have the same annihilation photon energy of 511 keV. For SPECT, the need for downscaling to individual single photon energies adds to the complexity.

The energy dependency of (mass) attenuation coefficients for all elements is different but well known [38, 39], and the mass attenuation of a compound material or mixture is determined by its elemental composition alone, each element having its own dependency on energy. Overall, the mass attenuation cross-section at the energies relevant to CT and SPECT is dominated by the sum of Compton scattering σ_c and photoelectric absorption τ, while pair production κ cannot occur (see Fig. 12).

Compton scattering is almost independent of the atomic number (Z) and has a low dependency of the photon energy (E), while photoelectric absorption depends strongly on both Z (power of 3–4) and E (power of −3). At  effective CT energies of 50–80 keV, and for the soft tissue components, Compton scatter alone is of significance, while for bone the photo absorption is important too (see Fig. 13).

2.3.2. Models for attenuation correction calculation from CT data

Each pixel of a CT image represents a mixture of elements, and the same composite value (in HU) can in principle result from different underlying mixtures of unknown elemental composition and densities. Therefore, the problem of energy translation does not have a strictly unique mathematical solution free of assumptions. Empirical approaches have been shown to solve the problem adequately in most situations. However, exceptions can lead to artefacts, which are covered in subsequent sections.

It is evident from Fig. 13 that a simple scaling with one common HU-to-μ value factor cannot account for the difference in materials, even among homogeneous pixels. A segmentation of the CT volume into the two major components of bone and non-bone (soft tissue), assigning a single SPECT μ value to each of the two domains, on the other hand cannot itself reflect the fact that both types of tissue can still have very different densities (e.g. in the lung volume the density is only ~0.3 g/cm³).

The common way to resolve this is to use a pixel wise scaling via a bilinear function (see Fig. 14). It represents the μ value as a continuous and unique function of HU and, therefore, does not require image segmentation. The method generally assumes the presence only of air (−1000 HU), water or soft tissue (~0 HU) and bone (~1000 HU). 

The lower part of the curve (line) intercepts at zero attenuation and therefore represents a simple scaling corresponding to the density of a mixture of air and soft tissue. The upper curve (line) represents a mixture of soft tissue and bone. The separation point corresponds to pure soft tissue (of density ~1 g/cm³) and the slope accounts for an increasing amount of compact bone (~1.9 g/cm³) in the mixture. Originally proposed only for use with the highest available CT energy (voltage 140 kV) to minimize the scaling factors and the effects of their potential uncertainties, it has later been generalized to variable CT energy as well as to variable SPECT photon energy [40].

0.1 1 10 100 1000

10 100

μ (c m

)

E (keV)

Bone Soft Tissue Ti

Fe

Iodine contrast Ba-contrast Au

Hg

99m

Tc

I

FIG. 13. Linear attenuation coefficients (cm⁻¹) for some materials of interest in SPECT/CT. At low energy (mainly photo absorption), compact bone and soft tissue differ by an order of magnitude owing to differences in Z; at higher energies (Compton scattering), they differ only by the density factor (<2). Two contrast media (iodine and barium), two typical metals for prostheses (titanium and iron) and elements for dental work (mercury and gold) are shown (see also Table 1, Section 2.3.2). In CT contrast materials (iodine and barium) and in metallic implants or dental work, photo absorption is dominant for CT as well as for 140 keV photons.

FIG. 12. Diagram with (E,Z) dependency of mass attenuation coefficients. The two ‘curtain edges’ are formed by curves representing the points in an (E,Z) diagram where two of the interaction cross-sections τ, σ and κ are equal. The horizontal dashed line (Z ≈ 7) shows that, for soft tissue, Compton scattering is dominating between 20 keV and 25 MeV. The vertical line at 140 keV shows that, for

99mTc, Compton scattering is the more important effect up to Z = 30. The line at 511 keV (PET) is shown for comparison.

Once the μ map is known, it can be included as part of the system matrix in the loop of an iterative reconstruction (e.g. attenuation weighted OSEM). Violation of the assumptions by the presence of other materials (e.g. contrast agents and metal) can result in image artefacts, which are shown and discussed in later sections.

Various proprietary extensions of the conversion methods have been introduced to reduce these effects. Table 1 shows linear attenuation values at a CT effective energy of 80 keV, at 140 keV (^99mTc) and 364 keV (¹³¹I), as well as the CT to SPECT ratios, the ‘downscaling factor’, for some tissues and materials of interest.

FIG. 14. Translation of HU to linear attenuation coefficients at 140 keV for SPECT (based on Ref. [40]). Example of an implementation of the bilinear method for three CT energies (given as kV) and conversion to SPECT (140 keV).

TABLE 1. LINEAR ATTENUATION COEFFICIENTS FOR CT AND SPECT

Material Density

(g/cm³)

μ (cm⁻¹) Ratio (downscaling factor)

80 keV 140 keV 364 keV 80/140 80/364

Soft tissue 1.06 0.193 0.162 0.116 1.20 1.67

Compact bone 1.92 0.428 0.295 0.198 1.45 2.17

Ti (Z = 22) 4.5 1.83 0.794 0.427 2.30 4.27

Fe (Z = 26) 7.8 4.64 1.67 0.770 2.77 6.03

Iodine contrast 1.3 1.23 0.401 0.151 3.07 8.15

BaSO₄ contrast 1.5 1.61 0.502 0.174 3.22 9.27

Au (Z = 79) 19.3 107 42.7 4.98 2.50 21.4

Hg (Z = 80) 13.6 71.5 30.8 3.58 2.32 20.0

Note: Mass attenuation values are calculated using XCOM [38] and multiplied by density to provide linear attenuation values. The composition and density of soft tissue and bone are from Ref. [41]. Values for the four elements shown (iron, gold, mercury and titanium) are for pure elemental material. The μ values at 80 keV for gold and mercury are  calculated as a mean of the values above and below the K edge. The values for the contrast agents are for the material before administration and dilution in the patient: the iodine contrast is an aqueous solution of a commercial product containing 300 mg/mL of iodine; and the barium contrast is a suspension in water containing 600 mg/mL of BaSO₄.

2.4. BENEFITS OF SPECT/CT